Iterative Refinement of Repeat Sequence Specification Using Constrained Pattern Matching

New algorithms for pattern matching with wildcards and length constraints

“…An interesting result in [22] is that online algorithms in [5,22] solve the DB case. Algorithms in [5,8,22,2] solve Table 1. Classification of the pattern matching with wildcards and length constraint problem into four groups.…”

“…Distinct letters in pattern (D) DU : [5,8,22,2] solve this case. Our solution for the DB case solves it as a special case in provably faster time.…”

“…the DU case. The time complexity of the algorithm for DU case in [8,2] depends on the complexity of the maximum flow algorithm used. The online algorithm in [5] takes Θ(|T | + k |P |g) time, where k is the frequency of P 's last letter occurring in T , is the user-specified maximum length for each matching substring (the global length constraint), and g is the maximum local gap of wildcards in P [5], i.e., g = max 1≤j<|P | {max j − min j }.…”

“…The problem has applications in sequential pattern analysis in data mining [17,20,25], in discovering patterns from biological sequences [24], and in finding repeating patterns in DNA [8]. The pattern matching with wildcards and length constraints problem can be stated as the following: Problem 1 ( [5]).…”

“…For example, let T = aabbbbcbc and P = aφ 3 1 bφ 2 0 c with global bounds of [minLen, maxLen] = [4,8]. The subscript and superscript on each φ specify the range of minimum and maximum number of wildcards between two literal matches (i.e., local length constraints).…”